Glueballs: hadrons without quarks

Abstract: Glueballs are colour-singlet bound states built from gluons alone. They are an unavoidable consequence of the non-Abelian structure of Quantum Chromodynamics (QCD), and, in the pure Yang--Mills limit, they are the only physical excitations of the theory. The present article reviews what is known about them. After establishing which spin, parity and charge-conjugation quantum numbers two- and three-gluon states can carry, the pure-gauge spectrum is surveyed. Each of the main theoretical approaches and their respective conclusions are briefly presented. They include lattice QCD, constituent-gluon and Coulomb-gauge models, functional Dyson--Schwinger and Bethe--Salpeter equations, holographic models, and QCD sum rules. Particular attention is paid to the scale-setting ambiguity that limits how precisely a quenched glueball mass can be converted into physical units. The discussion then turns to full QCD. After discussing the meaning of a glueball assignment in this context, unquenching effects and questions related to glueball--$q\bar{q}$ mixing are addressed. The large-$N_c$ counting that underpins the mixing picture, as well as mass-matrix and effective-Lagrangian treatments of mixing are presented. The selection rules and dynamical mechanisms that shape glueball decays are also discussed. The gluon-rich production mechanisms used experimentally are finally reviewed. The candidates are assessed sector by sector: $f_0(1370)/f_0(1500)/f_0(1710)$ and the competing interpretations of the scalar sector, $η(1405)/η(1475)$ and $X(2370)$ in the pseudoscalar sector, the crowded tensor region, and the essentially unexplored $C=-1$ sector and its connection to the Odderon. Outlooks on the programmes that could help in validating some of these candidates or identifying others are reviewed as a conclusion.